Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14581702 | C2 | semidirect |
| 3. C2×C8×Dic83 | C2 | semidirect |
| 5. #19127455 | C2 | semidirect |
| 6. #19127455 | C2 | semidirect |
| 10. C2×#13050574 | C4 | semidirect |
| 22. C22⋊C8×C83 | C4 | semidirect |
| 76. C2×Dic83 | M16 | semidirect |
| 80. C83⋊C8 | C22⋊C4 | semidirect |
| 105. C83 | #1753 | semidirect |
| 124. C22⋊C8 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050574 | 2 |
| C2×#14581702 | 2 |
| C2×C8×Dic83 | 2 |
| C4×C22⋊Dic83 | 2 |
| #19127455 | 2 |
| C2×C22⋊C8×C83 | 2 |
| #1753 | 83 |